Continuum mechanics analysis of fracture progression in the vitrified cryoprotective agent DP6.

As part of an ongoing effort to study the continuum mechanics effects associated with cryopreservation, the current report focuses on the prediction of fracture formation in cryoprotective agents. Fractures had been previously observed in 1 ml samples of the cryoprotective agent cocktail DP6, contained in a standard 15 ml glass vial, and subjected to various cooling rates. These experimental observations were obtained by means of a cryomacroscope, which has been recently presented by the current research team. High and low cooling rates were found to produce very distinct patterns of cracking. The current study seeks to explain the observed patterns on the basis of stresses predicted from finite element analysis, which relies on a simple viscoelastic constitutive model and on estimates of the critical stress for cracking. The current study demonstrates that the stress, which results in instantaneous fracture at low cooling rates, is consistent with the stress to initiate fracture at high cooling rate. This consistency supports the credibility of the proposed constitutive model and analysis, and the unified criterion for fracturing, that is, a critical stress threshold.

Analysis of the effect of partial vitrification on stress development in cryopreserved blood vessels.

Thermal stress development in blood vessels, during processes associated with vitrification (vitreous means glassy in Latin), is studied. This paper addresses the limiting case where the specimen completely crystallizes, while the cryoprotectant medium (CPA) completely vitrifies. This case is expected to provide upper boundary estimates for stresses for the more common problem of a partially vitrified sample. The CPA is modeled as a linear viscoelastic medium, with viscosity increasing exponentially with decreasing temperature; given the assumption of complete crystallization, the blood vessel is modeled as linear elastic below the freezing temperature. Consistent with previous observations, the CPA is found to behave linear elastically below a set-temperature, at which point the viscosity rises sufficiently quickly with further cooling. This observation reduces computational efforts and allows for parametric studies based on suitably chosen wholly elastic models. Both 2D concentric cylinder models of the blood vessel in a straight configuration and a 3D model of the vessel curled in a vial of CPA are studied; 2D models are shown to bound the results of the more general 3D problem. It is found that stress in the CPA decreases with increase in CPA volume, at least under conditions where the temperature can be viewed as uniform. Planar cracks are predicted to form transverse to the vessel axis, and to propagate right up to the blood vessel wall. Should such cracks propagate into the vessel, even over only a few mum, the mechanical damage to the lumen, or to endothelial cells, may cause the blood vessel to completely loose its functionality at the end of the cryopreservation protocol.

The Effect of Temperature Gradients on Stress Development During Cryopreservation via Vitrification.

This study addresses the problem of thermal stress development in bulky specimens during cryopreservation via vitrification (vitreous means glassy in Latin). While this study is a part of an ongoing effort to associate the developing mechanical stress with the relevant physical properties of the cryopreserved media and to its the thermal history, the current paper focuses exclusively on the role of temperature gradients. Temperature gradients arise due to the high cooling rates necessary to facilitate vitrification; the resulting non-uniform temperature distribution leads to differential thermal strain, possibly resulting in cracking. The cooling rate is assumed constant on the outer surface in this study, and the material properties are assumed constant. It is demonstrated that under these assumptions, mechanical stress develops only when the temperature distribution in the specimen approaches thermal equilibrium at a cryogenic storage temperature. It is shown that the maximum possible stresses for a given cooling rate can be computed with a simple thermo-elastic analysis; these stresses are associated with cooling to sufficiently low temperatures and are independent of the variation of viscosity with temperature. Analytic estimates for these stresses are obtained for several idealized shapes, while finite element analysis is used to determine stresses for geometries used in cryopreservation practice. Stresses that develop under a wider range of storage temperatures are also studied with finite element analysis, and the results are summarized with suitable normalizations. It is found that no stresses arise if cooling ceases above the set-temperature, which defines the transition from viscous-dominated to elastic-dominated behavior; the set-temperature is determined principally by the dependency of viscosity upon temperature. Strategies for rapidly reaching low temperatures and avoiding high stresses are inferred from the results.

Fracture formation in vitrified thin films of cryoprotectants.

As a part of an ongoing effort to study the continuum mechanics effects associated with cryopreservation, the current report focuses on fracture formation in vitrified thin films of cryoprotective agents. The current study combines experimental observations with continuum mechanics analysis. Experimental results have been developed using a new imaging device, termed a "cryomacroscope", which has been recently presented by the current research team. A newly developed liquid nitrogen-based cooling stage is presented in this paper. The samples under investigation are 0.5 ml droplets of cryoprotective agents, having a characteristic diameter of 20 mm and a characteristic thickness of 1.5 mm. Tested samples included dimethyl sulfoxide (DMSO) in a concentration range from 6 to 8.4M, and the cryoprotectant cocktails VS55 and DP6. Some samples contained small bovine muscle segments, having a characteristic dimension of 1mm, in order to study stress concentration effects. Experimental results show that the onset of fracturing in vitrified films of cryoprotectants is very consistent, occurring over a small temperature range. Fracture pattern, however, was affected by the cooling rate. The presence of tissue segments did not affect the onset temperature of fracture, but affected the fracture pattern. The continuum mechanics analysis solidified the hypothesis that fracture is driven by thermal stress, not by temperature per se, and allowed fracture strain to be inferred from observed fracture temperature. In conjunction with the current report, additional photos of fracture formation in thin films are available at .